I wouldn't call the sport AT software "better".
Simply, it has programming that allows for quicker shifts over the stanard AT. The faster shift programming likely comes into play in DS mode and likely during full manual mode.

Shift times for the standard AT I haven't found.
I have found specs for the sport AT describing the faster shifts.
Single gear up shifts 200 milliseconds. As fast as DCT.
Down shifts can occur in 100 milliseconds, faster than DCT.
Plus, sport AT allow for non sequential down shifts, so you can go from 6th to 3rd without having to shift down to 5th, then 4th, then 3rd.
That's another benefit over DCT, which has to do some sequential down shifts.

I'll post if I can find information on the standard AT.
It too is a great AT as it's really the SAME AT. The difference being shift times.

According to the new accel specs listed on BMW's website, the AT 0-60 has improved by .3 seconds for the 335i AT, and .1 for 328i AT.
Not sure why this happened as no power increase has been shown.
Maybe, they tested the sport AT this time and used the standard AT before? Can't be sure. We need more info to know why accel has improved for the AT.

Thanks RPM90 - great post.

I've decided to go with the sports automatic on the basis of rational, thought out advice like yours.

An earlier poster tried to polarise the debate by saying the standard automatic is poor, which is just plain wrong.